Embroidery machines are generally controlled by programs. Generally, a separate program is required for each embroidery design. There are very few methods available which provide the ability to modify existing embroidery design programs, with such prior art systems, by way of example, consisting of systems which vary the parameters associated with a stitch pattern design in order to control stitching machinery, such as disclosed in U.S. Pat. Nos. 4,326,473; 4,821,662; 4,720,795; 4,352,334; 5,191,536; 4,807,143; 4,849,902. Some of these prior art systems are capable of scaling pattern sizes or making other modifications to existing pattern designs either input by the user or stored in memory. However, none of the prior art systems known to applicants is capable of creating a self-generating embroidery design pattern based on fractal geometry in which the user need only select the desired basic fractal shape, such as the von Koch snowflake, by way of example, and the desired number of repeats, nor such a system in which the self-generated pattern can be readily merged with an existing embroidery design pattern in an outline data format to provide the resultant embroidery machine pattern control codes for the embroidery machine. This is so despite the fact that fractal geometry per se is well known, such as described in Computer Graphics: Principles and Practice, 2nd Ed., at page 1020, and in an article entitled "A Unified Approach to Fractal Curves and Plants", by Dietmar Saupe, at pages 273-286 of The Science of Fractal Images, Springer-Verlage, New York 1988. Moreover, although our prior U.S. Pat. No. 5,270,939, entitled "Method for Modifying Embroidery Design Programs", issued Dec. 14, 1993, naming Brian Jeffrey Goldberg and Anastasios Tsonis as joint inventors thereof, the contents of which are specifically incorporated by reference herein in its entirety, discloses an efficient method for converting stitch data for embroidery design programs into condensed outline data which may be edited, modified and then converted back to stitch data, it does not provide the ability to create self-generating patterns based on fractal geometry which further enhances the flexability and utility of the embroidery machines which are being controlled.